The industrial linkages of China’s vanadium industry integrating the recovery stage and spatial correlations: Based on disaggregated and nested input-output model

Abstract

Vanadium is increasingly recognized as a strategic and critical mineral resource on a global scale. Despite possessing the world’s largest reserves, China’s vanadium industry continues to face constraints such as limited industrialization and inadequate deep-processing capabilities. Mapping key industrial linkages is crucial for clarifying upstream-downstream interactions and enhancing the sector’s core competitiveness. In this study, we develop a disaggregated, nested input–output (I–O) model to systematically characterize these interdependencies. Our analysis reveals that, through a “resource-processing-application” global collaborative network, China’s vanadium industry has established an industrial ecosystem centered in the Asia-Pacific region. This ecosystem is defined by multiregional interconnectedness and comprehensive chain coverage, which collectively drive industrial advancement. In terms of industrial positioning, the core dynamic stems from a bidirectional synergy between China’s steel and chemical sectors. Regarding regional collaboration, upstream supply is directly bolstered by Australia’s iron ore mining industry. Downstream market linkages are anchored by the steel industries of Japan and Republic of Korea, which serve as technical collaboration hubs, while an export-oriented network is sustained by construction demand in the Middle East and emerging markets across the Asia-Pacific. Furthermore, the sequence of “material input-refining processing-vanadium steel output” characterizes its transnational circulation pattern.

Graphical abstract

Keywords

vanadium industry / disaggregated and nested input–output (I–O) model / industrial linkages / spatial correlation effects

1 Introduction

Vanadium has been classified as a strategic and critical mineral by major economies including the United States, the European Union, Australia, Canada, Japan, and China. China dominates globally in terms of vanadium production, reserves, and consumption. As the world's leading producer, it has consistently contributed more than 50% of the global annual output over the past decade. According to the United States Geological Survey (USGS), total proven global reserves of vanadium metal stand at 22 million tons, with the largest deposits located in China, Russia, Australia, South Africa, Brazil, and the United States. China leads with estimated reserves of approximately 9.5 million tons (Gao et al., 2022). Data from the USGS and the International Vanadium Association further indicate that China accounted for 47% of global vanadium consumption in 2019, highlighting its dual role as the largest consumer and a central player in the international market. Despite possessing the world’s largest vanadium resource base, China’s industrialization and deep-processing capabilities remain underdeveloped (Graedel and Miatto, 2023). Thus, converting this resource advantage into industrial competitiveness has become a pressing priority (Huang et al., 2023). Addressing the core question- “How can resource advantages be transformed into industrial strengths”?-requires a systematic analysis of key industrial linkages. Specifically, it is essential to identify which countries, regions, and industries China’s vanadium sector relies on most critically, and to which countries, regions, and industries it provides the greatest contributions.

To address the aforementioned challenges, this study develops a disaggregated and nested input–output (I–O) model tailored to China’s vanadium industry to examine its global industrial linkages. Current research in this domain includes, for example, the disaggregation of rare earth elements based on China’s national I–O table (Zhang et al., 2022), and the refinement of the power sector to compile a updated electricity-specific I–O data set for China (Liang et al., 2023). Other scholars have pursued granular disaggregation of I–O tables while preserving the overall industrial structure ( Holý and Šafr, 2023). Building on these efforts, the present research extends the disaggregation framework for China’s vanadium industry by incorporating not only upstream raw material extraction and midstream to downstream production processes, but also the downstream recycling phase. With the growing emphasis on the circular economy, recycling has become an increasingly critical component of industrial systems and represents an essential dimension for comprehensive analysis. Moreover, inclusion of the recycling stage enables a full life-cycle perspective, which is fundamental to assessing the vanadium industry’s resource efficiency and environmental impacts. This integration of recycling within the I–O disaggregation framework constitutes a methodological advance over prior studies.

Following the disaggregation of China’s vanadium industrial sectors, this study performs a balanced integration of these sectors into a global input-output framework. Currently, two primary methodologies are employed for nesting within I–O models. The first approach utilizes aggregate figures from the global I–O model as control totals. Proportional shares of each Chinese province within the national total are derived using China’s domestic I–O table and customs data, yielding corresponding allocation coefficients. The Chinese portion of the global I–O table is then disaggregated according to these coefficients, followed by a row-column balancing adjustment via mathematical optimization to produce an embedded world I–O table (Meng et al., 2013). The second approach takes the national I–O table of China as the control total and leverages the global I–O model to determine structural coefficients between China and other economies. Import and export flows are allocated based on these coefficients, with subsequent matrix balancing techniques applied to achieve consistency, resulting in an embedded global I–O structure (Ni and Xia, 2016; Cao, 2024). While both approaches offer distinct advantages, they are limited to nesting pre-existing sectoral classifications without further disaggregation. In contrast, this study conducts nesting based on newly disaggregated industrial sectors, enabling the incorporation of any sufficiently documented and quantitatively substantial sector into the global I–O framework. This approach significantly enhances analytical flexibility and granularity. Finally, the model undergoes technical validation to ensure robustness. Thus, this research extends and refines previous methodological efforts by introducing a more adaptable and detailed nesting procedure.

Following the disaggregation and nesting of sectors within China’s vanadium industry, this study conducts a deeper analysis of its industrial linkages. The concept of industrial linkage, originally introduced by Guitton (Guitton, 1957) through input-output methodology, has been widely applied in economic and industrial research. Recent studies have explored industrial linkages at both national and regional levels, covering a variety of dimensions. Some scholars have investigated the correlation between China’s foreign trade and industrial structures (Li et al., 2024), while others have examined interregional industrial transfer and spillover effects within China’s textile sector (Li et al., 2022). Further research has focused on sector-specific industrial interactions, such as the linkages associated with China’s air transport industry (Nian, Dong, 2022. Additional studies have addressed the spatial correlation between green finance development and industrial structure upgrading (Zhao et al., 2022), the relationship between ICT and energy consumption (Zhong et al., 2022), and conducted comprehensive dynamic evaluations of industrial ecological performance, including regional disparities and spatial correlations (Zhou and Chen, 2022). Moreover, spatial correlation analysis has been used to assess how industrial agglomeration and energy intensity affect industrial eco-efficiency (Zhong et al., 2023). Building on this existing body of work, the present study introduces spatial factors by integrating spatial correlation effects with conventional linkage analysis, enabling the identification of key industrial relationships with greater contextual and geographical relevance. This combined approach provides a more nuanced understanding of industrial networks and extends the methodological scope of previous research in the field.

In summary, the key innovations of this study are the construction of an I–O model for China’s vanadium industry, the refinement of I–O model disaggregation methods, and the identification of key industrial linkages within the vanadium sector. Specifically, this study develops a disaggregated I–O model for China’s vanadium industry and integrates it with a balanced nesting approach, embedding it into the global I–O model. This allows for an analysis of the industrial linkages between China’s vanadium industry and other domestic industries, as well as its linkages with different industrial sectors in other countries or regions. Furthermore, this study incorporates spatial factors by integrating spatial correlation effects with industrial linkages, enabling the identification of key industrial relationships. In addition, the remainder of the paper is organized as follows: Section 2 outlines the research methodology and data sources; Section 3 presents the empirical results and provides a detailed discussion; and Section 4 concludes the study.

2 Methods and data

Based on an analysis of China’s vanadium industry chain, this study employs the global I–O model to first disaggregate China’s vanadium industry sector and then embed it in a balanced manner into the global I–O model. This approach enables an analysis of the industrial linkages between China’s vanadium industry and other domestic industries, as well as its connections with industries in other countries and regions. The key indicators of industrial linkages include forward linkages, backward linkages, ripple effects, and the industrial spatial linkage index. After quantifying the major industrial linkages, this study integrates spatial correlation effects to identify the key industrial linkages, as illustrated in Fig. 1. In summary, this section identifies the key industrial linkages of China’s vanadium industry by combining the I–O model with spatial factors.

2.1 Construction of the I–O model

The upstream production of China’s vanadium industry primarily relies on vanadium-titanium magnetite, which accounts for approximately 87.3% of the supply. Vanadium-titanium magnetite is a type of iron ore. Additionally, about 93.99% of the downstream products in China’s vanadium industry are vanadium iron products and metal products, collectively referred to as vanadium steel products. According to data from the China Iron and Steel Association (CISA), the International Vanadium Association (Vanitec), and the World Steel Association, from 2015 to 2022, vanadium steel products accounted for an average of about 35% of China’s total crude steel production, as shown in Fig. S1 in support information. Therefore, the overall production volume and scale of China’s vanadium industry (from upstream vanadium-titanium magnetite to downstream vanadium steel products) are considered medium-sized industries and can exist as a separate industrial sector in the I–O table (Chen and Yang, 2011).

In this study, China’s vanadium industry is treated as a unified entity, referred to as China’s vanadium industry. The industry is disaggregated based on previous methodology (Zhang et al., 2022; Liang et al., 2023). Specifically, the upstream vanadium ore is disaggregated from the “Mining of iron ores” sector in the I–O table, and the midstream and downstream production is disaggregated from the “Manufacture of basic iron and steel and of ferro-alloys and first products thereof” sector. Additionally, this study innovatively incorporates the recycling stage by disaggregating the vanadium recycling portion from the “Recycling of waste and scrap” sector, which is a novel contribution of this research. In “support information”, we applied the System Dynamics and dynamic Material Flow Analysis model to evaluate two scenarios (A: without recycling; B: with recycling) and performed a terminal recycling participation rate sensitivity analysis. The results demonstrate that incorporating recycling enhances scientific rigor and significantly impacts ore demand, carbon footprint, and economic viability.

After completing the disaggregation of these three components, they are merged to form China’s vanadium industry sector, as illustrated in Fig. 2. Since this study examines the relationships between China’s vanadium industry and various global industries, the analysis is based on the global I–O table. The disaggregated vanadium industry is then balanced and nested into this global framework using appropriate methods (Yang et al., 2020; Ren et al., 2022), as illustrated in Fig. 3. In summary, this section combines disaggregation and nested balancing, indicating that as long as an industrial sector’s production volume and scale are sufficiently large, the production capacity and scale correspond to a small- to medium-sized industrial sector (Chen and Yang, 2011), researchers can analyze it using this research paradigm, even if it is not an existing sector in the current I–O table. This approach represents a significant contribution of this study.

The total output of China’s vanadium industry consists of the combined outputs from three components: the output from upstream vanadium ore production, the output from midstream and downstream vanadium product manufacturing, and the output from downstream recycling. These three components are calculated based on their respective proportions relative to the total industrial output of the “Mining of iron ores,” “Manufacture of basic iron and steel and of ferro-alloys and first products thereof,” and “Recycling of waste and scrap” sectors (Zhang et al., 2022; Liang et al., 2023), as detailed below.

(1){TOV}_n=\frac{{TIOV}_n}{{TIO}_n}\times {TO}_n,

(2)TOV={\sum }_{n=1}^3{TOV}_n,

where {TOV}_n and {TIOV}_n represent the total output and industrial total output of the three components of China’s vanadium industry, with n=1,\dots ,3; {TO}_n and {TIO}_n represent the total output and industrial total output of the “Mining of iron ores,” “Manufacture of basic iron and steel and of ferro-alloys and first products thereof,” and “Recycling of waste and scrap” sectors, respectively.

The final demand categories include household consumption, government consumption, gross capital formation, and exports. Since households and the government do not directly consume vanadium ore and vanadium steel products, the final demand categories for household and government consumption in the vanadium industry are both set to zero. Then, the increase in capital formation of the vanadium industry is calculated using Eq. (3) (Zhang et al., 2022; Liang et al., 2023).

(3)IG=\left(OP-OC\right)\times \frac{TOV}{OP}+IM-EX,

(4)Y=IG+EX.

In Eqs. (3) and (4), IG represents the capital formation revenue of the vanadium industry; OP and OC denote the production and consumption of vanadium, respectively; IM and EX represent the import and export of the vanadium industry, respectively; and Y stands for final demand.

For the intermediate input of China’s vanadium industry, it is necessary to integrate the Life Cycle Assessment (LCA) method. Based on previous studies (Zhang et al., 2022; Liang et al., 2023), this study refers to the Life Cycle Inventory (LCI) data from the Chinese Life Cycle Database (CLCD) and Ecoinvent database, as well as existing research results, to calculate intermediate inputs. The LCI of representative products at each stage of the vanadium industry chain is quantified separately and then matched with the corresponding industries in the input-output table. Finally, the total intermediate input is obtained through aggregation.

(5)x_{iv}={\sum }_s\left({ep}_{si}\times {ADI}_s\right).

In this context, v represents the vanadium industry, i represents other industry sectors in the input-output table, and s represents the five different stages of the vanadium industry chain. x_{iv} denotes the intermediate input of the other sectors for vanadium industry, {ep}_{si} refers to the unit value of the representative product from each stage of the vanadium industry chain in the LCI, and {ADI}_s represents the output of the corresponding sectors of these products.

The value of the vanadium industry for its own sector, x_{vv} is calculated based on the value of the representative products from each stage of the vanadium industry chain in the LCI. The intermediate output of the vanadium industry for other sectors is then calculated based on the proportional relationship of its downstream industry chain products (Zhang et al., 2022; Liang et al., 2023).

(6)x_{vv}=\sum _s{ep}_{sv},

(7)x_{vi}=\left(X_v-F_v\right)\times r_{pi},

In this context, {ep}_{sv} represents the value of the representative products at each stage of the vanadium industry chain corresponding to the vanadium industry in the LCI. x_{vi} denotes the intermediate output of the vanadium industry for other sectors, while X_v represents the total output of the vanadium industry, and F_v refers to the final demand. The value r_{pi} indicates the corresponding proportion of the downstream industry chain products of vanadium, sourced from data of the Vanadium Branch of the China Steel Industry Association (CSIA).

The approach involves disaggregating China’s vanadium industry and embedding it into the global framework, thereby analyzing the relationships between China’s vanadium industry and other global sectors (Yang et al., 2020; Ren et al., 2022). The specific methodology is as follows.

(8){Im}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}=\frac{{e\mathit{\text{z}}}_{ij}}{{im}_j},

(9){Ex}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}=\frac{{e\mathit{\text{z}}}_{ij}}{{ex}_i},

(10){Yim}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}=\frac{y_{ij}}{{yim}_j},

(11){Yex}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}=\frac{y_{ij}}{{yex}_i},

(12){N\mathit{\text{z}}}_j={Im}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}\times {ci}_j,

(13){N\mathit{\text{z}}}_i={Ex}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}\times {ce}_i,

(14){Ny}_j={Yim}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}\times {cy}_j,

(15){Ny}_i={Yex}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}\times {cy}_i.

{Im}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}, {Ex}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}, {Yim}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}, and {Yex}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}} represent the import and export ratios of intermediate use and final demand in EXIOBASE. {e\mathit{\text{z}}}_{ij} represents intermediate use, while y_{ij} represents final demand. {im}_j, {ex}_i, {yim}_j, and {yex}_i are the import and export quantities of intermediate use and final demand in EXIOBASE. N\mathit{\text{z}} and Ny refer to the nested intermediate use and final demand. {ci}_j, {ce}_i, {cy}_j, and {cy}_i represent the import and export quantities of China’s vanadium industry sector products.

For the disaggregated and nested balanced I–O model, we adopt the MRAS method from previous research to perform validation, which mainly involves three indicators to estimate matrix similarity. The Mean Absolute Percentage Error (MAPE) and Isard-Romanoff Similarity Index (DSIM) are relative distance measures. The Absolute PSI Statistic (ABSPSI) is a typical information-theoretic statistic used to assess the similarity between matrices. For all three measures, the smaller the value, the more similar the matrices are (Wiebe and Lenzen, 2016; Steen-Olsen et al.,2016; Chen et al., 2023). There are two points to note: first, the vanadium industry sector is excluded from the comparison because the original and new sectors cannot be compared using these indicators due to their different dimensions. Second, since {\mathit{\text{z}}}_{ij}^v and {\mathit{\text{z}}}_{ij}^o may be zero (and p_{ij} and q_{ij} may also be zero), not all metrics can always be directly calculated during the comparison process. Fortunately, the MRAS algorithm is a zero-preserving algorithm, which allows the corresponding elements to be zero. Therefore, when they cannot be calculated, we can confidently set them to zero. The specific model is as follows:

(16)MAPE=\frac{100}{m\times n}{\sum }_{i=1}^m{\sum }_{j=1}^n\left|\frac{{\mathit{\text{z}}}_{ij}^v-{\mathit{\text{z}}}_{ij}^o}{{\mathit{\text{z}}}_{ij}^o}\right|,

(17)DSIM=\frac{1}{m\times n}{\sum }_{i=1}^m{\sum }_{j=1}^n\frac{\left|{\mathit{\text{z}}}_{ij}^v-{\mathit{\text{z}}}_{ij}^o\right|}{\left|{\mathit{\text{z}}}_{ij}^v\right|+\left|{\mathit{\text{z}}}_{ij}^o\right|},

(18)ABSPSI={\sum }_{i=1}^m{\sum }_{j=1}^n{p}_{ij}\left|\mathrm{l}\mathrm{n}\left(\frac{p_{ij}}{s_{ij}}\right)\right|+{\sum }_{i=1}^m{\sum }_{j=1}^n{q}_{ij}\left|\mathrm{l}\mathrm{n}\left(\frac{q_{ij}}{s_{ij}}\right)\right|,

(19)p_{ij}=\frac{{\mathit{\text{z}}}_{ij}^v}{\sum _{i=1}^m\sum _{j=1}^n{\mathit{\text{z}}}_{ij}^v},

(20)q_{ij}=\frac{{\mathit{\text{z}}}_{ij}^o}{\sum _{i=1}^m\sum _{j=1}^n{\mathit{\text{z}}}_{ij}^o},

(21)s_{ij}=\frac{p_{ij}+q_{ij}}{2}.

In addition, Scenario Analysis and Uncertainty Analysis have been added in Appendix “support information” to ensure the scientific rigor and accuracy of the model.

2.2 Industry linkage model construction

To analyze the relationship between China’s vanadium industry and the industries of other countries and regions, this study examines it from the perspective of industry linkages, primarily through correlation coefficients. The first is the forward linkage effect, which reflects the driving force of a certain industry on various industrial sectors. Forward linkage measures the extent to which a particular industry, as a supplier of intermediate products, affects downstream industries. It reflects the widespread applicability of the products of that industry within the economic system and its contribution to the development of downstream industries. If the forward linkage coefficient of a certain industry is high, it indicates that the products it produces are important intermediate inputs for many other industries. In this study, forward linkage analysis focuses on the economic impact of China’s vanadium industry, as a supplier of intermediate inputs, on downstream industries (such as steel, chemicals, and construction). This is quantified through allocation coefficients and intermediate demand ratios. The total allocation coefficient represents the complete forward linkage relationship, while the direct allocation coefficient represents the direct forward linkage relationship. The direct allocation coefficient refers to the direct amount of i industry sector output allocated to the j industry sector for the production of products or services. The total allocation coefficient refers to the complete allocation amount of i industry sector output to the j industry sector’s production activities, including both direct and indirect allocations (Intarakumnerd and Jutarosaga, 2023). The direct allocation coefficient is as follows:

(22)R=\left\{r_{ij}\right\}=\frac{{\mathit{\text{z}}}_{ij}}{x_i},

where {\mathit{\text{z}}}_{ij} represents intermediate use, x_i represents the output of industry sector i.

The total allocation coefficient is as follows:

(23)H={\left(I-R\right)}^{-1}-I,

where I represent the identity matrix.

Intermediate demand ratio refers to the proportion of products from industry i that are used as intermediate products by other industrial sectors. A high intermediate demand ratio indicates that the industry is an intermediate goods industry, while a low ratio suggests that it is a final demand goods industry (Ventura et al., 2023).

(24)Q_i=\frac{{\sum _i^n\mathit{\text{z}}}_i}{x_i},

where {\mathit{\text{z}}}_i represents the total intermediate use of industry sector i.

Backward linkage indicates the pulling effect of a certain industry on various industrial sectors, which is quantified through consumption coefficients and intermediate consumption ratios. Backward linkage measures the degree of dependence of an industry on upstream inputs during its production process. It reflects the demand-pulling effect of the industry’s operations on the upstream supply chain. Industries with high backward linkage require stable and reliable supply chain support, and policies should focus on the development of upstream industries. Backward linkage analysis examines the extent of China’s vanadium industry’s reliance on upstream industries (such as mineral extraction, electricity, and transportation) during its production process. A higher backward linkage coefficient indicates a greater need for stability in the upstream supply chain for vanadium production. The total consumption coefficient represents the complete backward linkage relationship, while the direct consumption coefficient represents the direct backward linkage relationship. The total consumption coefficient is derived based on the direct consumption coefficient (Zhao et al., 2024).

(25)B={\left(I-A\right)}^{-1}-I,

where A represents the direct consumption coefficient matrix, and {\left(I-A\right)}^{-1} represents the Leontief inverse matrix.

Intermediate consumption ratio refers to the proportion of intermediate inputs to total inputs in the production process of industry j. A high intermediate consumption ratio indicates that the industry is a processing-type manufacturing industry, while a low ratio suggests that it is a factor-intensive basic industry (Zhao et al., 2024).

(26)P_j=\frac{{\sum _j^n\mathit{\text{z}}}_j}{x_j}.

Contagion effect and influence coefficient, sensitivity coefficient. The contagion effect refers to the impact of changes in one industry on other related industries, including the feedback effect on the industry itself. The contagion effect typically affects the entire national economic system. It is quantified externally through the influence coefficient and internally through the sensitivity coefficient. The influence coefficient F_j represents the extent of the impact that each new product from industry j has on other industries and production sectors. Its calculation formula is:

(27)F_j=\frac{\sum _{i=1}^n{l}_{ij}}{{\displaystyle \frac{1}{n}}\sum _{i=1}^n\sum _{j=1}^n{l}_{ij}}.

The sensitivity coefficient represents the total input required from industry i to increase one unit of final use in other industries (including its own industry) when all industrial sectors in the national economy increase by one unit of final use (Zhao et al., 2024). Its calculation formula is

(28){EI}_i=\frac{\sum _{j=1}^n{l}_{ij}}{{\displaystyle \frac{1}{n}}\sum _{i=1}^n\sum _{j=1}^n{l}_{ij}}.

In addition, this paper combines the abstract concept of industrial economic distance with linkage strength to construct an inter-industry spatial linkage index. The Average Propagation Length (APL) model uses the number of steps in the economic connections between industries as their economic distance. The smaller the APL, the shorter the economic distance between industries, and the fewer the intermediate links between industries. The shorter the economic distance, the higher the degree of linkage between different industries. The APL between industry i and industry j is defined as the weighted average number of steps required for the complete impact of industry j’s final demand to propagate to industry i (Dietzenbacher and Romero, 2007). The APL calculation formula is as follows (Yang et al., 2022):

(29){VI}_{ij}=\frac{a_{ij}+2[{A^2]}_{ij}+3[{A^3]}_{ij}+\cdots }{l_{ij}}.

Linkage strength represents the degree of connection between industries, as detailed below:

(30)G=\frac{B+H}{2}.

The inter-industry spatial linkage index. It is found that the closer the industry spatial linkage index is to 0, the stronger the spatial connection between one region (industry) and another region (industry). The inter-industry spatial linkage index constructed in this paper has three attributes: linkage strength, economic distance, and spatial layout. The specific formula is as follows:

(31){\delta }_{ij}^r=\frac{{\displaystyle \frac{{APL}_{ij}^r}{G_{ij}^r}}}{{\displaystyle \frac{{\overline{APL}}_{ij}}{{\overline{G}}_{ij}}}},

where r represents different regions, and i and j represent different industries. {\overline{APL}}_{ij} and {\overline{G}}_{ij} represent the corresponding means.

Based on this, this study combines spatial linkage effects (spatial factors) with industrial linkages to analyze and identify key industrial linkages. SL represents the spatial linkage effect. The larger the spatial linkage effect between China’s vanadium industry and other countries or regions, the more likely it is that there are close economic, technological, logistical, and policy connections between the two countries. These connections are reflected in aspects such as supply chain interdependence, technology sharing, regional cooperation, and environmental impact. Building on existing research, spatial linkage effects can further help us identify important industrial linkages for China’s vanadium industry. The spatial linkage effect can be expressed as (Liang et al., 2022; Yang et al., 2024):

(32)SL=\rho {\sum }_{j=1}^n{W}_{ij}{O}_j.

This paper uses the Gaussian function as the spatial variation function to calculate the weights between regions based on geographic distance:

(33)W_{ij}={\mathrm{e}}^{-\frac{d_{ij}^2}{2{\sigma }^2}},

where W_{ij} is the spatial weight matrix, and O_j represents the data of different industries in other industries of China or other countries or regions.

2.3 Data sources

The I–O related data comes from the EXIOBASE database version 3.8.2 (Konstantin et al., 2023), and the LCI data for the vanadium industry comes from the OPENLCA database. Industrial output data for the steel and vanadium industries is sourced from the CBC Metal Network, the Vanadium Division of the China Iron and Steel Association (CISA), the International Vanadium Technology Committee (Vanitec), and the World Steel Association's statistical data. Unit market prices for relevant materials or products are obtained from the CBC Metal Network, the Choice database, and the Wind database. The data covers the period from 2015 to 2022.

3 Results and discussion

3.1 Technical validation of the I–O model

The input-output data in this study involves 49 countries and regions, as detailed in the appendix. Except for China, the other 48 countries and regions each have 163 industrial sectors, while China has 164 industrial sectors due to the disaggregation of the vanadium industry sector. After embedding and balancing the vanadium industry sector of China into the global I–O model, we performed a technical validation of the overall model using the MRAS algorithm, and the results are shown in Table 1. Generally, the MAPE value ranges from 0 to 100. In this study, the average MAPE for all industrial sectors is estimated at 1.405, reflecting a high similarity between the two matrices. The average result of DISM for all industrial sectors is 0.004, which falls within the effective range. ABSPSI is an information-based indicator, and the average for all industries is 0.004. In summary, the adjustments made to the I–O model in this study minimize the impact on other intermediate flows, meeting the validation requirements. In addition to the MRAS (Row-and-Column Sums Adjustment) validation, local verification was also performed for the vanadium industry, primarily using the direct consumption coefficient validation method. Horizontal verificationconfirmed that the sum of intermediate inputs in each column equals the total input. Vertical verification demonstrated that the sum of intermediate uses in each row equals the total output. The of direct consumption coefficientswas validated to fall between 0 and 1. Based on these checks, the partial verification meets the required standards.

3.2 Forward and backward linkage analysis

The intermediate demand ratio represents the contribution of China’s vanadium industry in terms of its production output directly allocated to other industries for production. A higher intermediate demand ratio indicates that the industry is a supplier of intermediate goods, whereas a lower ratio suggests that the industry primarily produces final demand goods. Final demand goods refer to products or services that are directly aimed at end consumers or industries and meet their needs or desires. These goods or services are not further processed or resold but are directly introduced into the consumer market. As shown in Fig. S2 in Electronic Supplemenatry Material (ESM), the average intermediate demand ratio from 2015 to 2022 is approximately 0.3, showing a downward trend over the years. Therefore, China’s vanadium industry is classified as a final demand goods industry. The distribution coefficients are divided into direct distribution coefficients and full distribution coefficients, representing the amount of intermediate products directly and indirectly distributed through the upstream and downstream production chain relationships, allocated to all sectors of the national economy for production. This study selects the top 10 for China’s vanadium industry in terms of direct and indirect distribution coefficients for analysis. The main question being analyzed is which industries in which countries have directly or indirectly driven the development of China’s vanadium industry, or conversely, which industries have been directly or indirectly driven by China’s vanadium industry.

The results of the forward linkage analysis show (data for all years are shown in the ESM indicate that from 2015 to 2022) China’s vanadium industry directly drove the development of its domestic industries, such as the steel industry, chemical industry, and non-ferrous metals industry. At the same time, it also directly drove the development of the steel and metal products industries, construction, and machinery manufacturing in countries and regions such as Republic of Korea, other parts of Asia-Pacific, and the Middle East. From 2015 to 2022, the vanadium industry mainly drove the development of domestic industries, including non-metallic mineral products manufacturing, construction, machinery and equipment manufacturing, communication equipment and electrical manufacturing, other transportation equipment manufacturing, the aluminum industry, the steel industry, furniture manufacturing, and the chemical industry. The direct driving effect on China’s vanadium industry remained relatively stable between 2015 and 2022, primarily involving related industries in China and other parts of Asia-Pacific, including steel-related industries, construction, new chemicals, fossil energy industries, and machinery and equipment manufacturing. The indirect driving effects on China’s vanadium industry before 2018 were mainly from China, and after that, China, Australia, Brazil, South Africa, Canada, Turkey, other parts of Asia-Pacific, and Greece. The industries involved were primarily various power generation ation industries, iron ore mining, and the mining of other non-ferrous metals.

In summary, the direct driving effect is more significant than the indirect driving effect. China’s vanadium industry directly drives industries in parts of Asia and the Middle East, including steel-related industries, chemical industries, metal industries, manufacturing, and construction, all of which belong to the secondary industry sector. Indirectly, the industry mainly drives domestic secondary industries. The regions directly driving China’s vanadium industry are widespread, covering parts of Asia, the Americas, Africa, Europe, and Oceania, with industries mainly focused on steel and related metal ore mining and the power industry. After 2018, regions indirectly driving China’s vanadium industry were similar to those directly driving it, including parts of Asia, the Americas, Africa, Europe, and Oceania, with industries similarly focusing on steel and related metal ore mining and power generation.

The intermediate input ratio represents the proportion of other industries’ products required as intermediate goods for the production output of China’s vanadium industry. The higher the intermediate input ratio, the more raw materials the industry consumes, indicating a lower value-added rate. A high intermediate input ratio suggests that the industry is part of the processing manufacturing sector, while a lower ratio indicates it is a factor-intensive basic industry. As shown in Fig. S3 in the Electronic Supplementary Material, the average intermediate input ratio from 2015 to 2022 is approximately 0.021, with significant fluctuations. This also indicates that vanadium industry products have a higher value-added, making it a factor-intensive basic industry. In terms of classification, China’s vanadium industry is considered a resource-intensive industry, which heavily depends on natural resources in its production process. This is why the paper aims to establish an industrial advantage that matches its resource advantages. The consumption coefficients reflect the amount of products and services consumed by the products of other industrial sectors, producing a pull effect on these sectors. Therefore, the total consumption coefficient represents the complete backward linkage, while the direct consumption coefficient represents the direct backward linkage. This study analyzes the top 10 sectors in terms of direct and indirect consumption coefficients, investigating which countries’ industries have directly or indirectly pulled the development of China’s vanadium industry, or which industries have been pulled by the vanadium industry in different countries.

The results of backward linkage analysis show (data for all years are presented in the ESM that from 2015 to 2022) the steel and non-ferrous metals industries in China directly drove the development of China’s vanadium industry. Additionally, the steel products industries, chemical industries, and mechanical manufacturing industries in Republic of Korea, other regions in Africa, other regions in Asia and the Pacific, other regions in the Americas, and other regions in the Middle East also have a direct pulling effect. Before 2019, industries indirectly pulling the vanadium industry in China were mainly from China, Republic of Korea, other regions in Asia and the Pacific, other regions in the Americas, other regions in the Middle East, and other regions in Africa, particularly the steel and metal products industries. After 2019, industries primarily pulling the vanadium industry were in China and other regions in Asia and the Pacific, including the steel industry, metal products industry, mechanical manufacturing industry, and transportation sector. From 2015 to 2022, China’s vanadium industry directly pulled industries such as power transmission, iron ore mining, fossil energy extraction, mechanical manufacturing, and steel product manufacturing in countries including China, Australia, Brazil, Japan, other regions in the Middle East, Germany, and Republic of Korea. Before 2018, China indirectly pulled the development of industries such as the electricity sector, finance, fossil energy extraction, other commercial activities, electrical machinery and instrument manufacturing, and retail. Between 2018 and 2022, industries in China, Brazil, Japan, and Australia, such as iron ore extraction, the electricity industry, steel industry, construction, fossil energy extraction, and mechanical manufacturing, were indirectly driven by China’s vanadium industry.vanadium industry.vanadium industry.

In summary, direct pulling effect coefficients are superior to indirect pulling effects. The regions directly pulling China’s vanadium industry include Asia, the Americas, Africa, and the Middle East, with key industries such as steel-related industries, chemical industries, metal industries, and manufacturing. Indirect pulling forces are mainly from Asian countries, particularly involving metal manufacturing and steel-related industries. China’s vanadium industry has directly pulled the development of various regions in Asia, Oceania, the Middle East, and the Americas, particularly in industries like fossil energy and related metal ore extraction, metal manufacturing, and electricity. The main indirect pulling effects of China’s vanadium industry are observed in Asian countries, mainly in the electricity and steel-related industries.

3.3 Ripple effects and industrial space correlation index analysis

Ripple effects involve the influence coefficient and the sensitivity coefficient. Influence Coefficient refers to the relative level of impact when China’s vanadium industry increases unit final demand, affecting the output demand of various industries in the national economy. When the influence coefficient is greater than 1, it indicates that the industry’s influence exceeds the average influence level of all industries. The sector with the highest influence coefficient is considered the leading industry in the national economy, having a significant driving role in the overall economy. As shown in Fig. S4 and S5 in the Electronic Supplementary Material, the influence coefficient of China’s vanadium industry averaged 0.51 from 2015 to 2022, which is less than 1, meaning it does not exceed the average influence level of all industries, and thus it is not a leading industry. Sensitivity Coefficient measures the relative level of responsiveness of the vanadium industry to the demand for increased final output in the national economy. When the sensitivity coefficient exceeds 1, it indicates that the industry’s responsiveness to demand is higher than the average level of all sectors. The sector with the highest sensitivity coefficient is regarded as the foundational industry in the national economy, significantly constraining the overall economy. The sensitivity coefficient for China’s vanadium industry averaged 0.52 from 2015 to 2022, which is also less than 1, indicating that it is not a foundational industry. Furthermore, both the influence coefficient and the sensitivity coefficient have remained stable from 2015 to 2022, without significant fluctuations. In conclusion, China’s vanadium industry is neither a leading industry nor a foundational industry, which highlights the need to establish its industrial advantages.

The spatial association index between industries reveals that the closer the index is to 0, the stronger the spatial association between one region (industry) and another region (industry). The results show (results for all years are presented in the Electronic Supplementary Material) from 2015 to 2022, the countries most closely associated with China’s vanadium industry include Japan, Republic of Korea, other regions of Asia and the Pacific, other regions of the Middle East, and other regions of Africa, which are primarily located in Asia, the Middle East, and Africa. The industries involved include the extraction of fossil energy and related metal ores, metal manufacturing, and steel-related industries, all of which are secondary industries.

Based on the above, the relationship between China’s vanadium industry and other industries in China from 2015 to 2022 is shown in Fig. 4. China’s power transmission directly and indirectly drove the development of the vanadium industry, which in turn directly drove the steel industry, chemical industry, and other non-ferrous metal production industries, and indirectly drove the development of China’s construction industry, related metal manufacturing industries, and so on. For other countries and regions, the iron ore mining in Australia, Brazil, South Africa, and Canada directly and indirectly drove the development of China’s vanadium industry, while the metal ore mining industry in Turkey and other Asia-Pacific regions directly drove China’s vanadium industry. Meanwhile, China’s vanadium industry directly drove the construction industry and related metal manufacturing industries in Republic of Korea, other Asia-Pacific regions, and other Middle Eastern regions.

As shown in Fig. 5, China’s vanadium industry directly and indirectly pulled the development of China’s power transmission industry, indirectly pulling industries such as power generation, distribution, power trading, and electrical machinery manufacturing in China. Meanwhile, China’s steel industry and non-ferrous metal production industry directly and indirectly pulled China’s vanadium industry. Additionally, China’s metal manufacturing industry indirectly pulled the development of China’s vanadium industry. Regarding other countries and regions, China’s vanadium industry directly pulled the iron ore mining and related fossil energy mining industries in Australia, Brazil, Japan, and other Middle Eastern regions. The related metal manufacturing industries in Republic of Korea, other Asia-Pacific regions, other African regions, other American regions, and Middle Eastern regions directly pulled the development of China’s vanadium industry.

3.4 Identification of key industry linkages

The results of the spatial correlation effect show that China has the closest spatial correlations with Australia, Japan, Republic of Korea, other Middle Eastern regions (Saudi Arabia, UAE, Iran, and Egypt), and other Asia-Pacific regions (Mongolia, Malaysia, Singapore, Thailand, Vietnam, Pakistan, Bangladesh, Kazakhstan, and Uzbekistan). Introducing spatial correlation effects can better capture the dynamic interactions of the vanadium industry in the international market, helping to optimize import-export strategies and production planning. Through the industry spatial correlation index, it is possible to quantify and identify the countries or regions that play a key role in the development of the vanadium industry, avoiding the inclusion of too many low-correlation variables in the model, thereby improving modeling efficiency. Therefore, this method helps to focus on the key external factors that significantly affect the development of China’s vanadium industry, while enhancing the explanatory power and predictive accuracy of the model. Combining the basic industry linkage relationships and the industry spatial correlation index mentioned above, this study identifies the key industry linkages for China’s vanadium industry. It should be noted that Section 3.2 has proven that direct industry linkages are stronger than indirect linkages. Therefore, this study chooses direct industry linkages for the next step of the research. The key industry linkages for China’s vanadium industry are shown in Fig. 6. Specifically, there are 11 key linkages: The direct driving effect of the China’s steel industry on China’s vanadium industry; The direct driving effect of China’s vanadium industry on China’s chemical industry and steel industry; The direct pulling effect of China’s vanadium industry on Australia’s iron ore mining industry; The direct driving effect of China’s vanadium industry on Republic of Korea’s basic steel industry; The direct pulling effect of China’s vanadium industry on Japan’s basic steel industry; The direct pulling effect of China’s vanadium industry on Republic of Korea’s iron ore mining industry; The direct driving effect of China’s vanadium industry on the construction industry in other Middle Eastern regions; The direct driving effect of China’s vanadium industry on the construction industry in other Asia-Pacific regions; The direct driving effect of Australia’s iron ore mining industry on China’s vanadium industry; The direct pulling effect of the basic steel industry in other Middle Eastern regions on China’s vanadium industry; The direct driving effect of iron ore mining industries in other Asia-Pacific regions on China’s vanadium industry.

3.5 Discussion

Currently, China’s vanadium industry is neither a leading industry nor a fundamental industry; rather, it falls into the category of final-demand and factor-intensive industries. From a regional perspective, between 2015 and 2022, the regions with the closest industrial linkages to China’s vanadium industry include Australia, Japan, Republic of Korea, other Middle Eastern countries (Saudi Arabia, UAE, Iran, and Egypt), and other Asian and Pacific regions (Mongolia, Malaysia, Singapore, Thailand, Vietnam, Pakistan, Bangladesh, Kazakhstan, and Uzbekistan). Direct industrial linkages are stronger than indirect ones. By combining the industrial spatial association index with spatial association effects, this study identifies 11 key industrial linkages: The direct driving effect of the China’s steel industry on China’s vanadium industry; The direct driving effect of China’s vanadium industry on China’s chemical industry and steel industry; The direct pulling effect of China’s vanadium industry on Australia’s iron ore mining industry; The direct driving effect of China’s vanadium industry on Republic of Korea’s basic steel industry; The direct pulling effect of China’s vanadium industry on Japan’s basic steel industry; The direct pulling effect of China’s vanadium industry on Republic of Korea’s iron ore mining industry; The direct driving effect of China’s vanadium industry on the construction industry in other Middle Eastern regions; The direct driving effect of China’s vanadium industry on the construction industry in other Asia-Pacific regions; The direct driving effect of Australia’s iron ore mining industry on China’s vanadium industry; The direct pulling effect of the basic steel industry in other Middle Eastern regions on China’s vanadium industry; The direct driving effect of iron ore mining industries in other Asia-Pacific regions on China’s vanadium industry.

The regional and industrial linkage characteristics observed in China’s vanadium industry can be primarily attributed to its industrial nature and the global pattern of resource allocation. As a factor-intensive sector producing final demand goods, the vanadium industry does not occupy a leading or foundational position within the broader industrial system. Consequently, its development largely relies on a dual driving force: upstream resource supply and downstream application demand. On the one hand, China’s reliance on upstream vanadium resources has fostered strong connections with mining and basic steel industries in regions such as Australia, Republic of Korea, Japan, and the Middle East. On the other hand, the widespread application of vanadium in downstream sectors such as construction and chemicals has significantly stimulated the development of related domestic industries, particularly in regional construction sectors. Moreover, strengthened economic and trade cooperation with Asia-Pacific, the Middle East, and other regions under the framework of the Belt and Road Initiative has further reinforced vertical inter-regional industrial linkages.

In summary, this study systematically reveals the threefold development characteristics of China’s vanadium industry: First, in terms of industrial positioning, the vanadium sector functions as a factor-intensive industry that produces final demand goods. Its development momentum primarily stems from a dual transmission mechanism: forward-driven by the domestic steel industry and backward-supported by the chemical industry. Second, from the perspective of regional linkages, a multi-layered industrial network has been established with the Asia-Pacific region at its core. Upstream coordination with resource-rich countries such as Australia ensures stable raw material supply, while downstream export is driven by construction demand in emerging markets across the Middle East and Asia-Pacific. Third, in terms of value chain integration, the vanadium industry plays a key role as a “processing hub” in the global industrial chain. Through a cross-border cycle of “material input – refining and processing-vanadium steel output,” the industry effectively bridges primary resource extraction with end-use applications.

The 11 identified key vertical inter-industry linkages have built a well-structured industrial ecosystem for China’s vanadium sector. This ecosystem spans from abundant upstream vanadium ore resources, to efficient midstream production and processing, and to deep downstream integration with the steel, chemical, and construction industries-forming a complete and coordinated industrial chain. This multidimensional coordination not only stabilizes the supply of raw materials but also enhances the industry’s resilience and market competitiveness through strong material and product demand from related sectors such as steel. Leveraging this synergy, the future development of China’s vanadium industry should focus on technological upgrading and product sophistication. Priorities include the intensified R&D and industrialization of advanced vanadium-based alloys, vanadium-nitrogen alloys, and all-vanadium redox flow batteries. Furthermore, deepening cooperation with domestic and international partners in the steel, mining, and advanced materials sectors will be essential. This will support the extension of the vanadium industry chain toward intelligent, green, and internationalized development, thereby opening up broader market opportunities in high-end equipment manufacturing, energy storage, aerospace, and other strategic fields.

The industry sectors discussed in this paper that exhibit strong industrial linkages with China’s vanadium industry mainly refer to key sectors during the period from 2015 to 2022. Emerging high value-added industries, such as vanadium redox flow batteries, are not reflected in the quantitative analysis due to their currently low market penetration and limited production scale. However, these emerging sectors will be a key focus of future research.

4 Conclusions

Through a globally coordinated network of “resources-processing-applications,” China’s vanadium industry has developed an industrial ecosystem characterized by Asia-Pacific-centered dynamics, multi-regional collaboration, and full value chain coverage, thereby driving sustained industrial development. In terms of industrial positioning, as a factor-intensive industry producing final demand goods, the core momentum of China’s vanadium sector is driven by a dual transmission mechanism: forward linkage with the domestic steel industry and backward linkage with the chemical industry. Both domestic and international demand jointly stimulate capacity expansion. With respect to regional coordination, upstream resource security relies heavily on direct support from Australia’s iron ore mining sector. Midstream and downstream market integration is anchored in technological collaboration with the steel industries of Japan and Republic of Korea. Export-driven networks are further strengthened by construction demand in the Middle East (e.g., Saudi Arabia, the UAE) and emerging Asia-Pacific markets (e.g., Vietnam, Bangladesh).

In terms of value chain extension, the 11 identified key vertical inter-industry linkages indicate that China’s vanadium industry has established a transnational cycle characterized by “material input-refining and processing-vanadium steel output.” This is reflected in China’s upstream pull Australia’s iron ore sector, its downstream push for technological advancement in Republic of Korea’s steel industry, and its market penetration into the construction sectors of the Middle East and Asia-Pacific. Looking ahead, the industry is expected to expand into the fields of new energy and advanced manufacturing by focusing on the R&D and industrialization of high value-added products such as advanced vanadium-based alloys and all-vanadium redox flow batteries. Efforts should also be directed toward promoting green and globalized industrial chain development. At the same time, strengthening international technological cooperation-particularly in energy storage and advanced materials-will be essential for restructuring the global value chain toward greater intelligence and sustainability. Ultimately, this will enable the transition of China’s vanadium industry from a “processing hub” to an “innovation hub.”

5 Policy recommendation

Based on the analysis of 11 key vertical inter-industry linkages, policy efforts should focus on three strategic dimensions: strengthening the resilience of domestic industrial chains, constructing regional dual circulation between resources and markets, and enhancing China’s influence in global governance and rule-making. First, domestic industrial chain reinforcement should be prioritized. Vertical integration should be promoted through coordinated development of the vanadium-steel-chemical industries. Special funds should be established to support technological breakthroughs in vanadium extraction from low-grade ores and recycling technologies, aiming to improve domestic resource utilization and increase the penetration of vanadium in high-end steel products. Second, regional coordination must be advanced. This includes deepening “equity-for-mining-rights” cooperation with resource-rich countries such as Australia and Central Asian nations, and establishing joint reserves of vanadium-iron ores. Simultaneously, the Belt and Road Initiative should be leveraged to promote the export of Chinese standards for vanadium-based construction materials, aligning them with the infrastructure demands of the Middle East and Asia-Pacific regions. Third, rule-based leadership should be pursued. Mutual recognition of low-carbon vanadium product certifications can help China access high-end raw material markets in Japan and Republic of Korea. In parallel, China should collaborate with countries in the Middle East and Asia-Pacific to jointly establish regional vanadium recycling centers and take the lead in setting relevant international standards. In doing so, “vanadium diplomacy” can be embedded into multilateral cooperation frameworks. In summary, by forming an integrated policy framework that combines technology, market access, and rule-making, China can strategically shift from passive integration into global value chains to actively reshaping them. This would provide a practical model for enhancing China’s governance capacity over critical mineral resources.

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